A car traveled 75% of the way from town A to town B by traveling at T

Question

A car traveled 75% of the way from town A to town B by traveling at T hours at an average speed of V mph. The car travels at an average speed of S mph for the remaining part of the trip. Which of the following expressions represents the average speed for the entire trip?

A/ .75V+.25S
B/ .75T+.25S
C/ VT/3S
D/ 4VT/((T+S)/3)
E/ 4VS/ 3S+V

A. 0.75V + 0.25S
B. 0.75T + 0.25S
C. VT/(3S)
D. 4VT/(T+S)/3
E. 4VS/(3S+V)

gmat1220 · Accepted Answer

Let distance AB = 100 miles

75 miles @ V mph, time = 75/V
25 miles @ S mph, time = 25/S

Average speed = 100 /   = 4VS/ 3S+V

fluke · Answer

Let the distance between A and B be x.

T = 3/4* x/V
x = 4VT/3

Remaining distance = 0.25* VT/0.75 = VT/3

v_{avg} = Total Distance/(Time taken to travel 75%+Time taken to travel 25%)

v_{avg} = \frac{4VT}{3(T+\frac{VT}{3S})}

v_{avg} = \frac{4V}{3(1+\frac{V}{3S})}

v_{avg} = \frac{4VS}{(3S+V)}

Ans: "E"

Bunuel · Answer

Similar questions to practice: a-car-traveled-65-of-the-way-from-town-a-to-town-b-at-an-average-spee-219045.html a-car-traveled-75-of-the-way-from-town-a-to-town-b-at-an-149921.html

chowarth · Answer

Bunuel, I need help with this one. Can you please provide more detail to how you solved this problem? Thanks.

ScottTargetTestPrep · Answer

Solution:
 
The distance traveled at V mph is TV. Since this is 75% of the total distance, the total distance is TV/0.75 = TV/(3/4) = 4VT/3. Furthermore, ¼(4VT/3) = VT/3 miles are traveled at a speed of S mph, so (VT/3)/S = VT/(3S) hours are spent on traveling at S mph. Since average speed = total distance/total time, we have:

Average speed = (4VT/3) / (T + VT/(3S))
Average speed = (4VTS) / (3ST + VT)

Average speed = (4VS) / (3S + V)

Answer: E

nicbo · Answer

Hey  ScottTargetTestPrep  thank you for your explanation! I struggle with this one: Why do we calculate 1/4 of (4VT/3). 1/4 of 3/4 is something different isn't it? I totally understand the rest, it would be really helpful if you could explain this one?

Thank you in advance.

ScottTargetTestPrep · Answer

Remember that the total distance is 4VT/3. We know that 75% = 3/4 of this distance was traveled at a rate of V mph, so the remaining part was 1 - 3/4 = 1/4 of the total distance. Since we are told that the remaining distance was traveled at 5 mph, we take 1/4 of 4VT/3.

Jitesh8 · Answer

looking for easy to understand kind of solution to such problems

0Lucky0 · Answer

Hmm, Let me give it a try.

Average Speed = \frac{Total Distance}{Total Time} Average Speed = \frac{D}{(T₁ + T₂)} Since, T₁ = \frac{0.75D}{V}. and, T₂ = \frac{0.25D}{S}. So substituting these, we get: \frac{D}{ }. = \frac{D}{D }. = \frac{VS}{(0.75S + 0.25V)}. = \frac{VS}{ }. = \frac{4VS}{(3S + V). }. So, Answer is E. I hope this makes sense.

TargetMBA007 · Answer

karishma

I was wondering, if the average speed formula (2ab/a+b) can be applied in situations, where the distance is not equal, IF, we calculate the individual speeds first, for e.g. 
75/v and 25/s here?

I know this is not a suitable approach here, as the answers need variables, but I wonder if this approach would work in another question, where we needed the average speed as a value?

KarishmaB · Answer

No, we cannot use 2ab/(a+b) when the distances are not equal. It will get modified as per the fraction of the distance covered at each speed and hence, we should use the basic formula Avg Speed = Total Distance/Total Time. The 2ab/(a+b) is derived from this very basic formula.

Assuming total distance is d,  AvgSpeed = \frac{d}{\frac{3d/4}{v} + \frac{d/4}{s}} = \frac{4vs}{3s+v}

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A car traveled 75% of the way from town A to town B by traveling at T

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